Relating to magnified image formation systems, we consider two processes in this work: quantum and classical incoherent imaging. There are similarities and differences between them. A similarity is that the optical transfer functions (OTFs) of both systems are obtained by calculating a correlation function. Concerning the differences, only two were found. The first difference is that, unlike classical incoherent imaging, quantum imaging with photon pairs generated by spontaneous parametric down-conversion is sensitive to the phase in the function which describes the object. The second difference is that the OTF of the quantum imaging system is a cross-correlation function of the OTFs of the signal and idler arms, while the OTF of the classical incoherent imaging system is an autocorrelation of the only pupil function existing in this case. We explore experimentally the second difference. We report the observation of a highly resolved image produced by a quantum light source in a setup where an incoherent light source is unable to spatially resolve the image of the object. The spatial resolution of the image is studied in a situation where the size of the object is magnified at the image.
Relating to magnified image formation systems, we consider two processes in this work: quantum and classical incoherent imaging. There are similarities and differences between them. A similarity is that the optical transfer functions (OTFs) of both systems are obtained by calculating a correlation function. Concerning the differences, only two were found. The first difference is that, unlike classical incoherent imaging, quantum imaging with photon pairs generated by spontaneous parametric down-conversion is sensitive to the phase in the function which describes the object. The second difference is that the OTF of the quantum imaging system is a cross-correlation function of the OTFs of the signal and idler arms, while the OTF of the classical incoherent imaging system is an autocorrelation of the only pupil function existing in this case. We explore experimentally the second difference. We report the observation of a highly resolved image produced by a quantum light source in a setup where an incoherent light source is unable to spatially resolve the image of the object. The spatial resolution of the image is studied in a situation where the size of the object is magnified at the image.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.
It is well known that entangled-photon pairs generated by spontaneous parametric down-conversion exhibit a property that is analogous to that of ordinary incoherent lights. We formulate an image-forming optical theory of quantum lithography that comprehends the both conceptions of partial coherence and partial entanglement by extending a classical image-forming optical theory. Our optical system consists of an image-forming system, an illumination system with a second-order nonlinear medium, and two-photon absorbing materials. We evaluate the resolution of the quantum lithography system by using the optical transfer function and show a special case to be a super-resolving system.
Abstract. The field of Quantum Imaging exploits the quantum nature of light and the intrinsic parallelism of optical signals to devise novel techniques for optical imaging and for parallel information processing at the quantum level (see [1] and references quoted therein). In this presentation, we will shortly discuss two topics in this area: the first is the so-called ghost imaging which, however, is not necessarily quantum; the second is the detection of faint amplitude objects with a sensitivity beyond the standard quantum limit, and in this case we are fully in the quantum domain. Both topics are related to the phenomenon of optical parametric down-conversion (PDC), in which a fraction of the pump photons of a laser beam, injected into a crystal with a quadratic non-linearity, are down-converted to a pair of signal and idler photons, with conservation of total energy and total momentum. A feature of paramount importance is that the signal and idler beams are spatially correlated both in the near field (position correlation) and in the far field (momentum correlation).The simultaneous presence of position and momentum correlation implies quantum entanglement, as it has been also observed experimentally [2]. 1. Ghost Imaging
We present another step in our efforts to expand far-field imaging beyond the diffraction limit and beyond the limitations imposed by fluorescent labels. The model system we examine is based on the exploitation of entangled photon pairs at 810 nm generated by spontaneous parametric down conversion (SPDC) of a 405 nm source to resolve the separations of the line pairs of a series of two-dimensional objects. A ghost-imaging optical system directs signal and idler photons along two paths, one of which contains the objects. Images are constructed using a covariance analysis of the entangled pairs using typically 106 frames collected with an EMCCD detector that was calibrated to account for the number of entangled pairs of photons, which is necessary for an accurate determination of the resolution and its comparison with the classical method. Conservation of momentum requires that there is inversion symmetry between the transverse k vectors of the photons passing through the target and their entangled counterparts directed along the targetless path. Our covariance analysis not only addresses this symmetry but also that the width of the covariance peak is broader than a single pixel owing to the nature of SPDC and the details of the optical arrangement. Consideration of this broadening provides significant improvement of the image quality. The Heisenberg limit (HL) is achieved within experimental error: using the same optical alignment, the resolution obtained with entangled pairs of 810 nm photons is, within experimental error, twice that obtained with classical 810 nm photons. More importantly, the error bars of measurements with 810 nm entangled pairs are quantified by the Cramér-Rao lower bound (CRLB) and compared with those of the classical measurements. While other workers have done quantum imaging on nonpoint sources, to our knowledge we are the first group that not only has done the quantum imaging but also has compared the CRLB and the measured error of the quantum and classical measurements for a series of different-sized objects. (Similar comparisons have, however, been made for systems that can be approximated as point sources, e.g., determining the separation of two laser beams).
Ghost imaging can be performed using either quantum or classical states of light that possess strong spatial correlations. In both cases, the image is formed by averaging over many optical events. Here we show that it is possible to distinguish an object from a preestablished basis set of objects by using a small number of position-correlated photon pairs produced by spontaneous parametric down-conversion. The signal photon is incident on one member of a set of spatially nonoverlapping objects. The "ghost" image information is impressed upon the spatially separated idler photon and is extracted by means of holographic filtering and coincidence detection. We were able to distinguish among sets of two and four spatially nonoverlapping objects with confidence levels higher than 87% and 81%, respectively. This method of ghost imaging can be performed in situations requiring extremely low light levels.
Image resolution of quantum imaging with undetected photons is governed by the spatial correlations existing between the photons of a photon pair that has been generated in a nonlinear process. These correlations allow for obtaining an image of an object with light that never interacted with that object. Depending on the imaging configuration, either position or momentum correlations are exploited. We hereby experimentally analyse how the crystal length and pump waist affect the image resolution when using position correlations of photons that have been generated via spontaneous parametric down conversion in a nonlinear interferometer. Our results support existing theoretical models for the dependency of the resolution on the crystal length. In addition, we probe the resolution of our quantum imaging scheme for varying pump waists over one order of magnitude. This analysis reveals the intricate dependency of the resolution on the strength of the correlations within the biphoton states for parameter combinations in which the crystal lengths are much larger than the involved photon wavelengths. We extend the existing models in this parameter regime to properly take nontrivial effects of finite pump waists into account and demonstrate that they match the experimental results.